Absolute stability analysis for negative-imaginary systems. (May 2016)

• Record Type: Journal Article
• Authors: Dey, Arnab; Patra, Sourav; Sen, Siddhartha
• Is Part Of: Automatica. Volume 67(2016)
• Page Start: 107
• Page End: 113
• Publication Date: 2016-05
• Subjects: Lur'e system -- Slope-restricted nonlinearity -- Absolute stability -- Negative-imaginary system -- Positive feedback -- Lyapunov function; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.01.029
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper deals with absolute stability of a Lur'e system with positive feedback where the linear subsystem exhibits negative-imaginary frequency response and the nonlinearity connected in feedback is time-invariant, memoryless and slope-restricted. The proposed absolute stability criterion requires the linear subsystem to belong to the strongly strict negative-imaginary class. Along with that, positive definiteness of a symmetric matrix needs to be ensured, where the symmetric matrix is obtained by subtracting the dc-gain matrix of the linear subsystem from a strictly positive diagonal matrix with elements indicating the reciprocal of the maximum slope bounds of the nonlinearities. The stability criterion is proved using a Lur'e–Postnikov -type Lyapunov function. Numerical examples are presented to demonstrate the proposed results.